The sum of the lengths of any two sides of a triangle is gre

The sum of the lengths of any two sides of a triangle is greater than the length of the third side. what can you conclude about AC in triangle ABC??

AC+BC>AB, AB+BC>AC, AB+AC>BC . BC+AC =22, AB+BC=12. Answer is AC is less than 32/3.

Solution

solution

given

BC+AC=22

AC=22-BC

AB+BC=12

AB=12-BC

AB < BC + AC (since any side is less than the sum of the other 2 sides)

AB<22

12-BC<22

-BC<22-12

-BC<10

BC>10

BC+AC=22

AC= 12

AB+BC=12

AB= 2

so we can say that AB+BC=AC

AC+AB>BC